Optimal sensor placement and ensemble Kalman inversion for multiphysics reactor state estimation

• Developed a computational framework for parameter estimation and state reconstruction in multiphysics nuclear systems using ensemble Kalman inversion (EnKI). • Integrated average D-optimal experimental design for optimal sensor placement, enabling accurate inference from sparse, noisy measurements. • Employed Gaussian process regression to construct surrogate models, significantly reducing computational cost while preserving predictive accuracy. • Demonstrated robust estimation of key reactor parameters (velocity, power, heat transfer coefficient) in a one-dimensional molten salt reactor model. • Validated the proposed approach through extensive numerical experiments, showing effective calibration and state recovery under varying noise and computational constraints. This work presents a computational approach for parameter inference and state reconstruction, applied to a one-dimensional, physics-based model of a nuclear energy system. Accurate estimation of internal reactor parameters is hindered by limited sensor coverage and the inability to directly measure key internal quantities. To address this, we formulate an inverse problem for a steady-state molten salt reactor loop model governed by coupled neutron diffusion and heat transport equations. Experimental observations of temperature and thermal neutron flux are incorporated using an average D-optimal experimental design, which identifies the most informative sensor placements from a predefined sensor library. Parameter inference is performed using ensemble Kalman inversion (EnKI), a derivative-free ensemble-based method that iteratively updates parameter estimates using statistical corrections. To reduce computational cost, Gaussian process regression is employed to construct surrogate models of the forward model. Numerical experiments demonstrate that the proposed approach yields accurate and robust estimates of key physical parameters, enabling effective model calibration and uncertainty quantification in nuclear reactor applications.